Slowly varying function method applied to quartz crystal oscillator transient calculation

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

Volumn 45, Issue 2, 1998, Pages 520-527

  Brendel, Rémi ^a   Ratier, Nicolas ^b   Couteleau, Laurent ^a   Marianneau, Gilles ^b   Guillemot, Philippe ^a  

^a CNRS   (France)

^b CNES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; COMPUTER SOFTWARE; DIFFERENCE EQUATIONS; NONLINEAR EQUATIONS; POLYNOMIALS; QUARTZ; TIME DOMAIN ANALYSIS;

SOFTWARE PACKAGE SPICE;

CRYSTAL OSCILLATORS;

EID: 0032010771     PISSN: 08853010     EISSN: None     Source Type: Journal    
DOI: 10.1109/58.660161     Document Type: Article

References (12)

1. R. Brendel, G. Marianneau, and E. Robert, Nonlinear modelling techniques for quartz crystal oscillators, Proc. 5th European Freq. Time Forum, Conseil Général du Doubs, Besançon, Prance, 1991, pp. 377-384.
2. R. Brendel, G. Marianneau, T. Blin, and M. Brunet, Computer aided design of quartz crystal oscillators, IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 42, no. 4, pp. 700-708, 1995.
3. N. Ratier, R. Brendel, T. Blin, G. Marianneau, and P. Guillemot, Nonlinear simulation of quartz crystal oscillators, Proc. 9th European Freq. Time Forum, Conseil Général du Doubs, Besançon, Prance, 1995, pp. 88-92.
4. M. E, Prerking, Crystal Oscillator Design and Temperature Compensation. New York: Van Nostrand Reinhold, 1978.
5. J.-J. Gagnepain and R. Besson, Nonlinear effect in piezoelectric quartz crystals, in Physical Acoustics, vol. XI. New York: Academic, 1975, pp. 266-278.
6. B. Char, K. Geddes, G. Gönnet, B. Leong, M. Monagan, and S. Watt, Maple V Language Reference Manual. New York: Springer Verlag, 1991.
7. N. Ratier, R. Brendel, and P. Guillemot, Quartz oscillators: deriving oscillation condition by symbolic calculus, Proc. 10th European Freq. Time Forum, 1996, IEEE, Brighton, UK, pp. 442-446.
8. N. Kryloflf and N. Bogoliuboff, Introduction to Nonlinear Mechanics (translated from the Russian). Princeton, NJ: Princeton Univ. Press, 1943.
9. N. W. McLachlan, Ordinary Nonlinear Differential Equations in Engineering and Physical Sciences, 2nd ed. Oxford: Clarendon Press, 1958.
10. A. A. Andronov, A. A. Vitt, and S. E. Khaikin, Theory of Oscillators, New Yok: Pergamon, 1966.
11. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vatterling, Numerical Recipes. Cambridge: Cambridge Univ. Press, 1989.
12. N. Ratier, L. Couteleau, R. Brendel, and P. Guillemot, Automatic formal derivation of the oscillation condition, submitted for publication.